Infinite TMz radiating source with realistic AZIM coating
To realize the anisotropic zero/low-index property mentioned above for the 5.8 GHz band, which is widely used for wireless local area network (WLAN) systems, periodic end-loaded dipole resonators (ELDRs) are employed . Meandering end-loading is used to provide a degree of miniaturization. The unit cell geometry and dimensions are shown in the inset of Fig. 1.8a. An anisotropic parameter inversion algorithm was employed to retrieve the effective medium parameters (?ry, ?rz, nrx) from the scattering parameters obtained from unit cell simulations . The retrieved ?ry , ?rz , nrx are shown in Fig. 1.8b. While ?ry and mrx are virtually nondispersive with values around 2.4 and 1, respectively, the ?rz curve crosses zero at 5.38 GHz. The value of ?rz remains positive and below 0.15 within a broad frequency range extending from 5.4 to 6.1 GHz. In this frequency band, p™ of the practical grounded dispersive MM varies from a near-zero value to 0.35. This geometry yields a broader low-index bandwidth compared to that of commonly used subwavelength electric LC (ELC) resonators  due to the lower quality factor provided by the large capacitance inherent in the meandered end-loadings.
Figure 1.8 Geometry of the ELDR unit cell. The dimensions are p = 6.5 mm, b = 5.35 mm, a = 0.7 mm, d = 0.508 mm, and g = 2.8 mm. The substrate material is Rogers RT/Duroid 5880 with a dielectric constant of 2.2 and a loss tangent of 0.009. (b) The retrieved effective medium parameters ?ry, srz, and prx.
Full-wave simulations were then carried out to investigate the ability of a finite AZIM coating to control the radiation of an infinite slot. As illustrated in Fig. 1.9a, three cases were considered: (A) a 1 mm wide slot covered by a single-layer MM slab consisting of 14 cells in the x-direction, (B) a 1 mm wide slot covered by a dispersive effective medium slab with the retrieved relative permittivity and permeability tensors, and (C) a 1 mm wide slot alone. The structures are infinitely long i n the y-direction with only the field components Hy, Ex, and Ez existing in the far-zone, corresponding to the TMz mode. The far-field patterns (normalized to the value of the slot alone at broadside) in the upper half-space are presented in Fig. 1.9b for the three cases at 5.4 GHz. It can be observed that for the slot alone, the radiated wave is maximum close to в = ±40° due to the diffraction caused by the finite size of the ground plane in the x-direction. However, the actual MM or the effective medium slab causes the beam maximum to be located at broadside with about 9-fold enhancement. The radiated beam is sharpened and the radiation in other directions is greatly suppressed compared to that generated by the slot alone. The enhancement of radiated power at broadside as a function of frequency is shown in Fig. 1.9c. It can be seen that within a broad frequency range from 5.2 to 6.4 GHz, the broadside radiation enhancement remains above 4.5-fold. The drop in the enhancement factor is caused by the dispersive nature of the leaky MM slab, as previously discussed. However, compared to conventional directive leaky-wave antennas, stable unidirectional radiation at broadside is achieved over a much broader bandwidth. Overall, the numerical simulations show that the proposed subwavelength AZIM coating provides an efficient way of suppressing commonly encountered edge diffraction. In addition, the good agreement achieved between the simulation results using the actual MM and the effective medium slab justifies the homogenization approximation employed here, which is assumed valid due to the subwavelength size of the unit cells.
Figure 1.9 Configuration of infinite array simulations for an actual AZIM coating, a dispersive effective medium slab, and the slot alone. The structures are infinite in the у-direction with a periodicity of 6.5 mm. The finite-sized perfect electric conductor (PEC) plane is 92 mm long in the x-direction (located under an AZIM coating with 14 cells). A perfectly matched absorbing slab is placed underneath the slots in the simulations to absorb the radiation in the -z half-space. (b) Normalized radiated power for the three cases at 5.4 GHz (i.e., close to the effective plasma frequency of the metamaterial). All the curves are normalized to Case C at broadside (в = 0°). (c) Normalized radiated power at broadside (в = 0°) as a function of frequency.